Sirendaoreji; Jiong, Sun Auxiliary equation method for solving nonlinear partial differential equations. (English) Zbl 1011.35035 Phys. Lett., A 309, No. 5-6, 387-396 (2003). Summary: By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation. Cited in 1 ReviewCited in 67 Documents MSC: 35C05 Solutions to PDEs in closed form 35L70 Second-order nonlinear hyperbolic equations Keywords:direct algebraic method; exact travelling wave solutions; symbolic computation PDF BibTeX XML Cite \textit{Sirendaoreji} and \textit{S. Jiong}, Phys. Lett., A 309, No. 5--6, 387--396 (2003; Zbl 1011.35035) Full Text: DOI OpenURL References: [1] Hereman, W.; Takaoka, M., J. phys. A, 23, 4805, (1990) · Zbl 0719.35085 [2] Wang, M.L., Phys. lett. A, 199, 169, (1995) [3] Parkes, E.J.; Duffy, B.R., Comput. phys. commun., 98, 288, (1996) [4] Tian, B.; Gao, Y.T., Eur. phys. J. B, 22, 351, (2001) [5] Gao, Y.T.; Tian, B., Comput. phys. commun., 133, 158, (2001) [6] Gudkov, V.V., J. math. phys., 38, 4794, (1997) [7] Fan, E.G., Phys. lett. A, 277, 212, (2000) [8] Elwakil, S.A.; El-labany, S.K.; Zaharan, M.A.; Sabry, R., Phys. lett. A, 299, 179, (2002) [9] Parkes, E.J.; Duffy, B.R.; Abbott, P.C., Phys. lett. A, 295, 280, (2002) [10] Sirendaoreji; Jiong, S., Phys. lett. A, 298, 133, (2002) [11] Malfliet, W., Am. J. phys., 60, 650, (1992) [12] Liu, S.; Fu, Z.; Liu, S.; Zhao, Q., Phys. lett. A, 289, 69, (2001) [13] Boussineq, J., Comptes rendus, 72, 755, (1871) [14] Toda, M., Phys. rep., 18, 1, (1975) [15] Zakharov, V.E., Sov. phys. JETP, 38, 108, (1974) [16] Scott, A.C., (), 80 [17] Ablowitz, M.J.; Segur, H., J. fluid mech., 92, 539, (1979) [18] Ablowitz, M.J.; Bar Yaacov, D.; Fokas, A.S., Stud. appl. math., 69, 135, (1983) [19] Boiti, M.; Leon, J.; Pempinelli, F., Inverse problems, 3, 371, (1987) [20] Paquin, G.; Winternitz, P., Physica D, 46, 122, (1990) [21] Tian, B.; Gao, Y.T., J. phys. A: math. gen., 29, 2895, (1996) [22] Lou, S.Y., Phys. lett. A, 176, 96, (1993) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.